I have heard that Ibn ‘Umar (radiyallahu ‘anhuma) use to pretend to relieve himself, without having the need to do so, at a particular place just to imitate Nabi (sallallahu ‘alayhi wasallam). Is this correct?

I have come across the following narration, does it give the same meaning?

It is possible that Sayyiduna ‘Abdullah ibn ‘Umar (radiyallahu’anhuma) would force himself to relieve himself, since it is far fetched that each time he passed this spot he genuinely had a call of nature.

Therefore the conclusion mentioned in your question is correct.

Translation

Anas ibn Sirin (rahimahullah) narrates we were with Sayyiduna ‘Abdullah ibn ‘Umar (radiyallahu ‘anhuma) at ‘Arafah. After zawal, I proceeded with him until he came to the Imam and prayed with him the Zuhr and ‘Asr. He then engaged in ‘ibadah (wuquf) and my companion and I did the same until the Imam departed. We departed with him until we reached a pass then he dismounted his camel and we dismounted and we thought he wanted to perform Salah. His servant that took hold of his conveyance, said that he does not intend to perform Salah but rather he remembered that when Nabi (sallallahu ‘alayhi wasallam) reached this place he relieved himself, so he (Sayyiduna ‘Abdullah ibn ‘Umar -radiyallahu’anhuma-) loves that he also relieves himself.